Suppose that Po is invested in a savings account in which interest is compounded continuously at 6.9% per year. That is, the balance P grows at the rate given by the following equation. dF = 0.069P(t) dt (a) Find the function P(t) that satisfies the equation. Write it in terms of Po and 0.069 (b)Suppose that $500 is invested. What is the balance after 1 years? (c)When will an investment of $500 double itself? (a) Crouse me collect answer below. O A. P(1) = P e 0.069t O B. P(1) = 0.069Pet O C. P. = P(1) e 0.0691 O D. P(t) = P(t) e 0.0681 (b) The balance after 1 year is S (Type an integer or decimal rounded to two decimal places as needed. ) (c) The doubling time is |year. (Type an integer or decimal rounded to two decimal places as needed.)